A hollow cylinder of length L has inner radius of R1 and outer radius of R2, as shown in the figure. The outer, curved s

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A hollow cylinder of length L has inner radius of R1 and outer
radius of R2, as shown in the figure. The outer, curved surface at
r = R2 is perfectly insulated, and the two end faces at z = 0 and
at z = L are also perfectly insulated. The cylinder is initially at
a temperature given by the 2-D distribution T = F(r, z). At t = 0,
convection heat transfer is initiated by flowing a cooling fluid
through the center hole with fluid temperature Too and with uniform
convection coefficient of h; hence convection heat transfer at the
inner surface r = R1.
(i) Solve for the transient temperature distribution.
(ii) Solve for the steady-state temperature distribution